Air quantity to blow up a tyre

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SUMMARY

The discussion focuses on calculating the air quantity required to inflate a tire to a specific pressure using the ideal gas law and related principles. The ideal gas equation, PV = mRT, is referenced, with R being the specific gas constant for air at 287 J/(kg*K). Participants emphasize that temperature and volume are not constant during pressurization, suggesting that an adiabatic process is more applicable than isothermal. The flow rate through the valve is influenced by viscous friction, making the Bernoulli equation unsuitable for this scenario; instead, the relationship between pressure drop and flow rate must be determined experimentally.

PREREQUISITES
  • Understanding of the ideal gas law (PV = mRT)
  • Knowledge of thermodynamic processes, specifically adiabatic and isothermal processes
  • Familiarity with flow rate calculations (Q = A*v)
  • Basic principles of fluid dynamics, including Bernoulli's equation
NEXT STEPS
  • Research the application of the ideal gas law in non-constant temperature scenarios
  • Study the principles of adiabatic processes and their impact on gas behavior
  • Explore experimental methods for quantifying the relationship between pressure drop and flow rate
  • Learn about viscous flow and its effects on fluid dynamics in pressurized systems
USEFUL FOR

Engineers, physicists, and anyone involved in fluid dynamics or tire inflation processes will benefit from this discussion, particularly those looking to apply thermodynamic principles in practical applications.

Andrea Vironda
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Hi
i would to know how to predict the air quantity need to blow up a definite-shaped object, like a tyre, to a certain pressure.
i would to apply the ideal gas law, i should obtain something like P/m=cost.
is it correct? i supposed temperature and volume constant
 
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Andrea Vironda said:
apply the ideal gas law
And the equation is...?
Andrea Vironda said:
supposed temperature and volume constant
The temperature will not be constant during pressurisation, but you can suppose it returns to the original temperature eventually.
 
Do you know the approximate internal volume of an inflated tire, or how it might be determined?
 
the Volume of a inflated tyre can be seen as a torus. The equation i would use is PV=mRT, with R the specific air constant, 287 J/(Kg*K)
at P_0=1 bar i have a certain air mass. if i double it, i'll double also the pressure. is it correct?
 
Andrea Vironda said:
if i double it, i'll double also the pressure. is it correct?

Yes, so long as the tyre has not expanded much.
 
i wish to calculate the flow passing from an high pressure source to the tyre. I think it is only function of ΔP.
should i use Bernoulli for finding speed and Q=A*v, [m3/s]?
 
Andrea Vironda said:
i wish to calculate the flow passing from an high pressure source to the tyre. I think it is only function of ΔP.
should i use Bernoulli for finding speed and Q=A*v, [m3/s]?
As I mentioned, you cannot assume constant temperature during pressurisation. The air will heat up, producing some pushback and slowing the flow. Not completely adiabatic, but probably closer to that than to isothermal.
 
I think adiabatic is better. but how can i link a thermodynamic process to the flow speed? if i use, for example, the P-T relation for an adiabatic process, i have not any info about speed
 
Andrea Vironda said:
I think adiabatic is better. but how can i link a thermodynamic process to the flow speed? if i use, for example, the P-T relation for an adiabatic process, i have not any info about speed
The flow through the valve is dominated by viscous friction, so the Bernoulli equation is not appropriate. The rate of flow through the valve is going to depend on the pressure difference across the valve. The relationship between pressure drop and flow rate needs to be quantified experimentally.
 

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